Thanks for your input. I will think about this. The most obvious kind of abstraction known to all of us is abstraction in the plastic arts, especially in the second half of the twentieth century. I have seen some attempts (can't remember where) to put modernist abstraction in arts to other movements, but I don't think anyone has done justice to this. Also, there is no guarantee that there is a fundamental relationship between abstraction in the formal sciences and abstraction in the arts. It is not uncommon for people to pick up a word (or even an idea) and use for however they like. Jacques Lacan did this with topology. That doesn't mean that there is a fundamental relationship between Lacanian analysis and topology.

Best wishes,

Nick